How do you graph y=√x+5, compare it to the parent graph and what is the domain and range?

1 Answer
Tony B
Feb 25, 2018

Domain x∈[−5,+∞)
Range y∈[o,+∞)

Explanation:

Assumption: The parent graph is y=√x

Although 'true' square root is ± it is not stated as such in the question. We only have + so this is what is called the principle square root. The condition ± produces the shape ⊂ so as we only have the positive half of the condition ± we end up with only the top half of the shape ⊂

For the value to NOT go into the complex number set of values the 'content' of the root must not become negative.

Thus the minimum value is such that x+5=0⇒x=−5.

The 'action' of changing y=√x to y=√x+5 'moves' the graph of y=√x to the left on the x-axis by 5.

The x-intercept is at y=0=√x+5 thus xintercept=−5
The y-intercept is at x=0⇒y=√5≈2.24 to 2dp
Domain x∈[−5,+∞)
Range y∈[o,+∞)

Tony B

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